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Jane and Mark Burry’s book exploring the interface between mathematics and architecture is vital to the future of architectural dialect, says Lionel March

Early in the 1970s, while working at Cambridge University’s Centre for Land Use, I was invited to meet the RIBA library committee. Members had identified a gap in the collection: there was no book on architecture and contemporary mathematics.

I learnt that Alison and Peter Smithson had been puzzled by the mathematics that their son was bringing home and they had alerted the committee to this. The book that my co-author Philip Steadman and I put forward, The Geometry of Environment (1971), introduced the fundamental terms of what educators were branding as the ‘new mathematics’ – mappings, euclidean transformations, sets, groups, relations, and linear graphs, among others.

The mathematisation of university subjects like geography, archaeology, anthropology, sociology and economics was in the Cambridge air and architecture did not escape the winds of change.

Engineering, of course, stood on a bedrock of mathesis. Designer Christopher Alexander, for example, had eschewed the architectural structures class, substituting plastic theory in engineering in its place. Thus, it comes as no surprise that authors of The New Mathematics of Architecture, husband-and-wife team Mark and Jane Burry, spent five years reading architecture in Cambridge at the turn of the 1970s and 80s.

The new ‘new mathematics’ in this must-have book picks up on developments over the last 40 years. Sixty of these advances are succinctly summarised in an illustrated 13-page glossary, from ‘acoustic optimization’ to the ‘Weaire-Phelan model’ of polyhedral packing. Such concepts are scattered through 46 architectural projects of international significance, presented through text, beautiful photographs and computer graphics.

Prefaces are usually ignored in reviews, but Brett Steele, director of the Architectural Association, deserves credit for his brief yet thoughtful essay. He remarks on the conscious application of ‘number’ in traditional architecture and its disappearance in the encoded depths of software, leaving, as he writes, ‘a very real void in the language of architecture’.

But he adds that the designers in this book show a ‘willingness to directly take on the challenge of reinventing the very language – and numbers – lying behind their surface’. Steele’s essay is followed by an introduction by Mark Burry, ‘Mathematics and Design’.

I have no disagreement with his brief historical review of mathematical tendencies and I am pleased to see his positive reference respecting surfaces to Le Corbusier’s chapel at Ronchamp and even more so to his Philips Pavilion.

Six chapters follow: mathematical surfaces and seriality; chaos, complexity, emergence; packing and tilings; optimization; topology; datascapes and multi-dimensionality. I wonder whether the Burrys considered an historical chapter on precedences in which such works as Le Corbusier’s might have been surveyed.

Burry himself is a practising authority on Antoni Gaudí and sections on the Sagrada Familia and Colònia Güell are included to remind us of the architect’s inverted chain models, optimising catenary structures.

This funicular technique is said to have been used to determine the impressive surface structure of the Main Station, Stuttgart, by Ingenhoven Architects: ‘When inverted and made rigid, this same surface shape distributes forces in pure compression, minimizing both the depth and the need for steel reinforcement in the shell.’

Its conception drew on work undertaken at the University of Stuttgart Institute for Lightweight Structures and Conceptual Design. Like so many schemes in the book, the station is illustrated in computer graphics, since this bold project is not expected to be completed until 2016.

Another is Jean Nouvel’s striking design for the Louvre Abu Dhabi. This project is covered by a 180m-diameter perforated dome. The translucency is achieved by ‘the superimposition of the layers of the structure and the internal and external cladding’.

A different form of translucency is achieved on the blue Watercube by PTW Architects for the Beijing Olympics, through the ethylene-tetrafluoroethylene skin on all five exposed faces of a simple cuboid. The skin emulates the packing of soap bubbles using a modification of the Weaire-Phelan polyhedral model.

If I were an administrator in an architecture institution, keen to recruit the brightest students to the profession, I would send a copy of this book to every sixth-form college in the land with compliments. It is an awesome turn-on. Perhaps, even better, it could find a life on the web.

Lionel March is emeritus professor of design and computation at UCLA

The New Mathematics of ArchitectureJane and Mark BurryThames & Hudson, October 2010, £32

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